To evaluate the geospatial hazard relationships between recent
(contemporary) rockfalls and their prehistoric predecessors, we compare the
locations, physical characteristics, and lithologies of rockfall boulders
deposited during the 2010–2011 Canterbury earthquake sequence (CES)
(n=185) with those deposited prior to the CES (n=1093). Population
ratios of pre-CES to CES boulders at two study sites vary spatially from ∼5:1 to 8.5:1. This is interpreted to reflect (i) variations in
CES rockfall flux due to intra- and inter-event spatial differences in
ground motions (e.g., directionality) and associated variations in source
cliff responses; (ii) possible variations in the triggering mechanism(s),
frequency, flux, record duration, boulder size distributions, and
post-depositional mobilization of pre-CES rockfalls relative to CES
rockfalls; and (iii) geological variations in the source cliffs of CES and
pre-CES rockfalls. On interfluves, CES boulders traveled approximately 100 to 250 m further downslope than prehistoric (pre-CES) boulders. This is interpreted to reflect reduced resistance to CES rockfall transport due to preceding anthropogenic hillslope de-vegetation. Volcanic breccia boulders are more dimensionally equant and rounded, are larger, and traveled further downslope than coherent lava boulders, illustrating clear geological control on rockfall hazard. In valley bottoms, the furthest-traveled pre-CES boulders are situated further downslope than CES boulders due to (i) remobilization of pre-CES boulders by post-depositional processes such as debris flows and (ii) reduction of CES boulder velocities and travel distances by collisional impacts with pre-CES boulders. A considered earth-systems approach is required when using preserved distributions of rockfall deposits to predict the severity and extents of future rockfall events.
Introduction
Rockfall deposits pervade many mountainous and hilly regions worldwide
(Varnes, 1978; Evans and Hungr, 1993; Wieczorek, 2002; Dorren, 2003;
Guzzetti et al., 2003) and can provide important data for assessing future rockfall hazards (Porter and Orombelli, 1981; Keefer, 1984; Dussauge-Peisser et al., 2002; Copons and Vilaplana, 2008; Wieczorek et al., 2008; Stock et al., 2014; Borella et al., 2016a). Their characteristics (e.g., location, size, and morphology) may be used to complement numerical rockfall modeling scenarios (Agliardi and Crosta, 2003; Dorren et al., 2004; Heron et al., 2014; Vick, 2015; Borella et al., 2016a) and inform engineering-design
criteria for rockfall mitigation structures (e.g., impact fences, tiebacks, and
protection forests) (e.g., Agliardi and Crosta, 2003; Dorren et al., 2004;
Guzzetti et al., 2004). However, natural and anthropogenic changes to the
landscape (including changes to the rockfall source and slope areas) between
successive rockfall events and the post-depositional history for rockfalls
can be complex (e.g., Borella et al., 2016a, b). To better understand how past
rockfalls provide suitable proxies for characterizing future hazard,
comparisons between the geologic and geomorphic attributes of individual
rockfall events and cumulative amalgamations of many events are valued.
Critical evaluations of possible intervening changes to the landscape that
may influence the mechanics of rockfall production and travel are an
important component of these studies.
More than 7000 mapped individual rocks fell from cliffs in the Port Hills in
southern Christchurch during the 2010–2011 Canterbury earthquake sequence (CES) in New Zealand's South Island (Massey et al., 2014). Most of the rockfalls (>6000) occurred during the 22 February 2011 moment
magnitude (Mw) = 6.2 and 13 June 2011 Mw=6.0 Christchurch earthquakes (Massey et al., 2014). Approximately 200 houses were impacted, 100 houses were severely damaged, and five fatalities occurred due to falling rocks in the 2011 February earthquake (Massey et al., 2014; Grant et al., 2017). CES rockfalls were characterized by boulder-size distribution, runout distance (the distance a rock travels down a slope from its source), source-area dimensions, and boulder-production rates over a range of triggering peak ground accelerations (Massey et al., 2012a–e, 2014, 2017; Mackey and Quigley, 2014; Quigley et al., 2016).
Subsequent field investigations revealed an abundance of pre-CES rockfall
deposits in CES rockfall areas (Townsend and Rosser, 2012; Mackey and Quigley, 2014; Borella et al., 2016a, b), suggesting multiple rockfall events had occurred at these sites in the past (Mackey and Quigley, 2014; Borella et al., 2016a, b; Sohbati et al., 2016). Retrospectively, these pre-CES deposits had the potential to contribute to hazard assessments during land planning and urban development in Christchurch prior to the CES; however, there is no evidence that they did so (Townsend and Rosser, 2012; Litchfield et al., 2016). At one well-studied location (Rapaki) in the Port Hills of southern Christchurch, CES and pre-CES boulder populations were shown to have similar volumetric size and morphology characteristics, but a significant population of CES boulders had longer maximum runout distances than their pre-CES counterparts (Borella et al., 2016a). Pre-CES rockfalls were dated using independent approaches to >3–15 ka (Mackey and Quigley, 2014; Sohbati et al., 2016; Borella et al., 2016b). With the aid of numerical modeling of rockfall trajectories (using RAMMS – rapid mass movement simulation) these data were collectively interpreted to suggest that anthropogenic deforestation between pre-CES and CES rockfalls was the primary cause for the observed spatial distinctions in CES and pre-CES rockfall distributions (Borella et al., 2016a). Elsewhere in the Port Hills and greater Banks Peninsula, the causes for differences in the spatial distribution between CES and pre-CES rockfalls are less clear and in some locations the current positions of pre-CES boulders extend further distances from source cliffs than their CES counterparts. A more integrated and regional understanding of the geologic, geomorphic, seismogenic, and
anthropogenic controls on rockfall distributions has the potential to inform
rockfall hazard analyses for land zoning and engineering considerations here
and elsewhere (e.g., Lan et al., 2010).
In this study we document the location, volume, morphology, and lithology
for individual (n=1093) pre-CES rockfall boulders at two sites (Rapaki and
Purau) in the Banks Peninsula near Christchurch, New Zealand. The spatial
distributions and physical attributes for pre-CES boulders are compared to
rockfall boulders (n=185) deposited at the same sites during the 2010–2011 CES. The RAMMS's bare-earth and forested numerical modeling scenarios are conducted to help evaluate the influence of natural and anthropogenic
factors on rockfall distributions, identify boulder sub-populations that
have likely experienced post-emplacement mobility, determine the relative
timing of pre-existing rockfalls (i.e., prehistoric or historic), and
evaluate the efficacy of RAMMS in replicating empirical CES and prehistoric
boulder spatial distributions. We highlight the complexity of interpreting
future rockfall hazard based on former boulder distributions (particularly
location) due to the following: (i) potential landscape changes including deforestation,
(ii) changes in rockfall source (e.g., progressive emergence of bedrock
sources from beneath sedimentary cover), (iii) remobilization of prior
rockfalls by surface processes including debris flows (primarily in
channels), (iv) lithological variability effects on the type of material
liberated in successive events, (v) collisional impedance with pre-existing
boulders (particularly in channels or valleys), and (vi) variations in the
location, size, and strong ground motion characteristics of past
rockfall-triggering earthquakes and their impact on rockfall flux and
boulder mobility. We use an integrated earth-systems approach, which
combines a consideration of geologic, geomorphic, seismogenic, and
anthropogenic influences on rockfall distributions with high-quality
field-based (i.e., prehistoric and contemporary rockfall data sets) and
instrumentally recorded (seismic) data sets, and numerical modeling. Our
results have broad implications for using rockfall distributions to forecast
future rockfall hazard.
Geologic settingOverview
Banks Peninsula, located on the east coast of New Zealand's South Island, is
comprised of three main volcanoes (Lyttelton, Akaroa, and Mount Herbert)
active between 11.0 and 5.8 Ma (Hampton and Cole, 2009) (Fig. 1). The two
study sites (Rapaki and Purau) are located within the inner crater rim of
the Lyttelton Volcanic Complex (Figs. 1–3), the oldest of the volcanic
centers and thought to be active from 11.0 to 9.7 Ma (Hampton and Cole,
2009). Source rock at both sites is classified by Sewell (1988) and Sewell
et al. (1992) as part of the Lyttelton Volcanic Group (LVG) and consists of basaltic to trachytic lava flows interbedded with breccia and tuff (Mvl). Numerous dikes and minor domes are observed within the LVG. Our field observations support the reported lithologic descriptions for the two study locales. The inferred strike and dip for lava flows nearest to the study sites indicates a shallow inclination in a predominantly northerly direction for measurements nearest the Rapaki and Purau study sites (Hampton and Cole, 2009). Sewell et al. (1992) report a similar shallow northerly to northwesterly dip of 12∘ for lava flows nearest Rapaki. The study areas were selected because both have abundant pre-CES and CES rockfall boulders (Fig. 4) derived from lithologically equivalent volcanic source rocks. Rapaki represents a case study location proximal to the source of the 2011 February and June Christchurch earthquakes (epicenters ∼2.5–5.0 km; hypocenters ∼5.6–7.0 km), while Purau is located more distally (epicenters ∼6.6–8.4 km; hypocenters ∼8.9–10.3 km). Estimated rockfall-generating peak horizontal ground velocities (PGV) at the Rapaki site in the February and June earthquakes were ≥30 cm s-2 (Mackey and Quigley, 2014).
The Rapaki study site is situated in the Port Hills of southern Christchurch
(Figs. 1 and 2) on the southeastern slope of Mount Rapaki (Te Poho o Tamatea), which has a summit height of ∼400 m. The study hillslope is slightly concave to planar with a total area of ∼0.21 km2 and
faces to the east-southeast. The source zone consists of steep to subvertical bedrock cliffs composed of stratified basaltic lava and indurated auto-breccia or pyroclastic flow deposits (Fig. 5a–c). Breccia layers are thicker (∼3–10 m) and jointing is more widely spaced (often >10 m). Coherent lava layers are comparably thin (<3 m) and joints are more closely spaced (generally <1–2 m). Total height and length of the source rock are ∼60 and ∼300 m, respectively (Fig. 5a). Below the
source area is a ∼23∘ grassy hillslope composed of windblown sediment deposits (loess), loess and volcanic colluvium, and overlying rockfall boulders (both CES and pre-CES) (Bell and Trangmar, 1987). Rapaki village (estimated population = 100 residents) lies at the hillslope base at elevations of ∼70 m a.s.l, to sea level (Fig. 2a and b). Anthropogenic deforestation has exposed a hillslope that is currently experiencing accelerated erosion (Borella et al., 2016a, b) in the
form of mass wasting and tunnel gully formation. Shallow landslides,
including debris and earth flows, are most prevalent in upper- to mid-slope
positions, while rill and gulley erosion predominate in lower-slope
positions. Rockfall is a dominant surface feature at the Rapaki study site
(Mackey and Quigley, 2014; Vick, 2015; Borella et al., 2016a, b). Pre-CES and
CES rockfall boulders at the study site are divided into two dominant
lithology types: volcanic breccia (VB) and coherent lava (CL) basalt. During
the 22 February and 13 June 2011 earthquakes, more than 650 individual CES
boulders ranging in diameter from <15 cm to >3 m were dislodged from the volcanic source rock near the top of Mount Rapaki, many impacting and destroying residential homes (Massey et al., 2014; Mackey and Quigley, 2014).
(a) Mapped pre-CES volcanic breccia (VB) and coherent lava (CL) boulders with volume ≥ 1.0 m3 at Rapaki. The largest boulders with the furthest runout distances are comprised exclusively of volcanic breccia. Ratio of pre-CES VB to CL boulders is ∼22:1. (b) Mapped CES VB and CL boulders at Rapaki study site. Note the low number of CL rockfall boulders detached during the CES at Rapaki. Ratio of CES VB to CL boulders is 15:1 (a : volcanic source rock; b : dominated by volcanic boulder colluvium and volcanic loess colluvium; c : loess colluvium underlain by in situ loess and volcanic rock; d : alluvial sediments overlying loess and bedrock).
Purau study site
Purau is located on the southern side of Lyttelton Harbour, approximately 5 km southeast of Rapaki (Figs. 1 and 3). Slopes at Purau have a
west-northwest aspect, the opposite of the Rapaki study hillslope. Mapping
of pre-CES and CES rockfall was performed on and within several interfluves
(spurs) and bounding valleys, respectively (Fig. 3) and encompassed a total
area of ∼1.4 km2. The source rock geology at Purau,
including lithology and structure, is equivalent to that observed at Rapaki
(Fig. 5d and e). The ridgeline (i.e., volcanic source rock) to the east obtains a maximum elevation of ∼440 m. Locally, individual vertical to subvertical bluff faces are estimated to be ∼20–30 m in height. From the base of the volcanic source rock, slopes extend downward toward Purau Bay at angles ranging from ∼30 to ∼5∘ near Camp Bay Road (Fig. 3). Field observations indicate the volcanic rock is overlain by loess, loess colluvium and volcanic colluvium, and pre-CES and CES rockfall boulders of small (e.g., <1 m3) to extremely large sizes (e.g., >100 m3). Deforestation of Purau slopes has left the hillside covered
primarily in low-lying grass and bush. Shallow slips are abundant and are
commonly observed on steep slopes, including valley flanks. Maximum
landslide depth is typically ∼1–1.5 m and often exposes volcanic bedrock at bottom, indicating the overlying sediment is relatively thin. Tunnel gulley erosion predominates on canyon flanks and at lower elevations.
MethodsField mapping and characterization of CES and pre-CES rockfall boulders
We mapped 1276 individual rockfall boulders at the Rapaki (pre-CES = 408;
CES = 48) and Purau (pre-CES = 684; CES = 136) study sites for boulder volume ≥ 1.0 m3 (see Supplement, Tables S1–S4,
10.5061/dryad.9km1t86). Where safety conditions permitted, pre-CES and
CES rockfall boulders were mapped to the base of the volcanic source rock.
Location (latitude and longitude) and elevation (meters above sea level) were
recorded for each rockfall deposit using a handheld Garmin GPSMap 62s
device. Boulder dimensions (i.e., height, length, and width) were tape measured
in the field. For pre-CES boulders partially buried to the degree that only
2 dimensions were adequately measurable, the shorter of the two measured
lengths was used for the 3rd dimension, thus insuring a conservative
boulder size estimate. No rounding factor was applied to volumetric
estimations of pre-CES boulders. The lithology type was determined for each
pre-CES boulder and was based primarily upon the observed dominant rock
“texture”. Boulder lithologies were categorized as VB or CL. Transitional
lithologies were rarely observed (<1 % of total) and assigned as VB or CL based on the volumetrically predominant rock type.
(a) Mapped pre-CES and CES rockfalls with volume ≥ 1.0 m3 at Purau study site. Ratio of pre-CES to CES boulders is ∼5:1 (a : volcanic source rock; b : dominated by volcanic boulder colluvium and volcanic loess colluvium; c : loess colluvium underlain by in situ loess and volcanic rock; d : alluvial sediments overlying loess and bedrock). (b) Mapped pre-CES VB and CL boulders at Purau. Ratio of pre-CES VB to CL boulders is ∼2:1. (c) Mapped CES VB and CL boulders at Purau study site. Note the low number of CL rockfall boulders detached during the CES at Purau. Ratio of CES VB to CL boulders is ∼14:1. PD1–PD4 represent Purau rockfall domains.
Boulder runout distance
Boulder runout distance was determined by measuring the shortest horizontal
and ground-length distances, perpendicular to slope contour lines, from the
nearest potential bedrock source areas to mapped boulder locations using
Google Earth Professional (Tables S5–S8, 10.5061/dryad.9km1t86). Runout distance was calculated for 409 pre-CES boulders and 48 CES boulders (for volume ≥ 1.0 m3) at Rapaki. Due to safety concerns we were unable to record locations for pre-CES boulders within ∼100 m (map length) of the volcanic source rock at this site. However, boulder frequency counts (for boulder volume ≥ 0.1 m3) were field measured within a 300 m2 area at distances of 0–10 m (n=31),
30–40 m (n=35), 60–70 m (n=77), and 100–110 m (n=24) from the volcanic source rock (see Fig. A1). The boulder frequency counts at these distances were used to extrapolate the number of boulders across remaining sections of the study site, consistent with visual inspection of air photos. At Purau, four separate geomorphic domains (PD1–PD4) were created to evaluate pre-CES and CES boulder runout distance (see Fig. 3; Tables S7 and S8, 10.5061/dryad.9km1t86). The domains include interfluve and valley morphologies, target areas with both CES and pre-CES rockfall boulders, and cases where the pre-CES rockfalls were sourced from a single or limited number of rock exposures. We generally report map length runout distance within this paper.
We used the empirical shadow angle method (Lied, 1977; Evans and Hungr,
1993) to analyze the travel distance of rockfalls at Rapaki and Purau. The
shadow angle is the arctangent of the relationship Ht/Lt, where Ht is the height of fall on the talus slope (elevation difference between the apex of the talus slope and final emplacement location of the rockfall block) and Lt is the travel distance on the talus slope (horizontal distance between the
apex of the talus slope and the final emplacement location of the rockfall
block) (see Copons et al., 2009; Lied, 1977; Evans and Hungr, 1993) (see Fig. A2). The shadow angle method is most suitable for our study
(compared to the reach or “Fahrböschung” angle) because it does not require
identifying the source release location for individual rockfall blocks, a
parameter we are unable determine for the pre-CES and CES rockfalls.
RAMMS rockfall modeling
Three model scenarios were conducted using the Rapid Mass Movements System (RAMMS) software (Bartelt et al., 2013; Leine et al., 2014).
RAMMS_1 represents a bare-earth CES model and was performed to test the reliability of RAMMS in replicating the spatial distribution for CES rockfalls at Purau. RAMMS_2 assumes a vegetated slope and simulates hillslope conditions prior to deforestation (i.e., prehistoric). RAMMS_3 models the potential future rockfall hazard at Purau and assumes a bare-earth (deforested) hillslope and dry soil moisture conditions to insure a worst-case (conservative) outcome. Please see Supplement for more detail on the individual RAMMS modeling scenarios.
The Purau terrain was modeled using a 4 m DEM (digital elevation model)
derived from LIDAR (light detection and ranging) surveys to model CES
(bare-earth scenario) and pre-CES (prehistoric forested slope scenario)
rockfall distributions. The rockfall boulders were modeled as rigid
polyhedral. The source areas (i.e., volcanic rock) and remaining runout
terrain types (i.e., loess and loess–volcanic colluvium) (Table A1 Figs. A4–A6) for the RAMMS model scenarios (i.e., RAMMS_1 to _3) were chosen following the methods of Vick (2015) and Borella et al. (2016a) and delineated as polygon (Fig. A4) and polyline (Figs. A5 and A6) shapefiles in
ArcGIS from field observations, desktop study of orthophotography, and
satellite imagery.
Boulder shape and size are highly influential in the dynamics and runout of
a rockfall event (e.g., Leine et al., 2014; Latham et al., 2008). Boulder
shapes and sizes used in the model simulations were representative of the
true boulder geometries observed at Purau and Rapaki (Borella et al.,
2016a). Rock shapes were created using the RAMMS “rock builder” tool, which creates boulder point clouds based on a user-defined shape and size. All boulder shapes reflected “real” rock bodies that have been field scanned. For each size class of boulder, varying shapes were selected, which are simplified to equant, flat, and long. Please see Supplement for more detail on boulder shape and size distributions utilized in each of the RAMMS modeling scenarios.
Vegetation was modeled in RAMMS as forest drag, a resisting force acting on
the rock's center of mass when located below the drag layer height. The
forest was parameterized by a drag coefficient, effective up to the input
height of the vegetation layer. Typical values for the drag coefficient
range between 100 and 10 000 kg s-1 (Bartelt et al., 2013; Leine et al., 2014). Vegetation was assigned an effective height of 10 m. A variable
forest density was applied to account for the presumed denser vegetation (on
average) within drainage valleys at the Purau study site (Fig. A7). We assume more surface and subsurface water would be focused into topographic lows and would therefore promote denser tree growth. Within drainage valleys a uniform drag force of 6000 kg s-1 was applied to each of the simulated boulders. Elsewhere at the study site, a drag force of 3000 kg s-1 was applied. These forest values are equivalent to those utilized in
Borella et al. (2016a) at Rapaki in the Port Hills of southern Christchurch.
We also simulated a uniform forest density increase of 10 000 kg s-1 (see Sect. 4). As evidenced by modern native forest analogs, tree growth was
extended upward to the base of the source rock and was also applied to areas
between outcropping volcanic source rock.
Strong ground motions near rockfall source cliffs
Strong ground motion accelerograms for stations LPCC, D13C, D15C, and GODS
were obtained from GeoNet (https://www.geonet.org.nz/, last access: 11 May 2019, Fig. 6) to analyze the influence of ground motion on rockfalls. All these stations are Kinemetrics Etna instruments except LPCC, which is a CUSP-3 instrument. LPCC recorded both the Mw=6.2 event on 22 February 2011 and the Mw=6 event on 13 June 2011. The other stations were installed following the Mw=6.2 earthquake and thus recorded only the Mw=6 earthquake. The data were sampled at 0.005 s (Nyquist frequency 100 Hz) and filtered with an effective passband having corners ∼0.05 and ∼40 Hz. We integrated accelerograms to produce velocity seismograms and computed envelopes using
ENV =[x(t)⋅2+H(x(t))⋅2], where x(t) are time points in the seismogram, and H is the Hilbert transform. The particle velocity hodograms are calculated in the horizontal plane by rotating the horizontal orthogonal components of the seismogram to a standard N–S E–W coordinate system. The time window of particle velocity hodograms is ±5 s around the peak of the envelope of the east component. This ensures that the most significant ground motion resulting from both phase and group velocity peaks is accurately captured. Following a similar procedure, we computed particle motion hodograms by integrating accelerograms twice. These are given in Fig. 7a–e. Additional methods were used to analyze D13C data following interpretation of initial results; these are described in Sect. 5.7.
ResultsRockfall mapping and boulder frequenciesRapaki
A comparison of the spatial distributions for pre-CES and CES rockfalls at
Rapaki (Fig. 2) indicates that pre-CES rockfalls are more concentrated near
the source area and have shorter maximum runout distances (560±15 m)
than the furthest traveled CES rockfalls (700±15 m) that impacted
Rapaki village during the 2011 Christchurch earthquakes. The CES rockfalls
represent a subset of the pre-CES rockfall data set; the ratio of pre-CES
(n=409) to CES (n=49) rockfalls at Rapaki is ∼8.5:1 (Fig. 2). The pre-CES and CES rockfall data sets are separated into VB and CL boulders (Figs. 2 and 4) to understand the influence of volcanic lithology on
rockfall runout and final resting location. Very few CL boulders with volume ≥ 1.0 m3 exist for pre-CES (n=18) and CES (n=3) rockfalls at Rapaki. Pre-CES and CES VB boulders display longer average and maximum runout distances than their CL counterparts (Fig. 2), and CES CL and VB boulders display longer average and maximum runout distances compared with
their pre-CES equivalents. The ratio of pre-CES VB to CL and CES VB to CL
rockfall boulders is ∼22:1 and ∼15:1, respectively (Fig. 2).
Pre-CES and CES VB boulders at Rapaki and Purau study sites. (a) Pre-CES boulder in footslope position with smaller CES boulder at right bottom. (b) Exploratory trenching exposes the colluvial sediment wedge at the backside (upslope) of the boulder. (c) Pre-CES boulder at Purau study site. Erosion of the surrounding hillslope sediments has exposed the boulder base and underlying loessic sediment. (d) Advanced surface roughness and abundant lichen growth on pre-CES boulder surface. (e) CES boulder (∼28 m3) detached from Mount Rapaki and emplaced in the Rapaki village during the 22 February 2011 earthquake (photo courtesy of D. J. A. Barrell, GNS Science). (f) CES boulder showing 2011 detachment surface (1) and adjacent non-detached surface (2) with higher degree of surface roughness. (g–k) Representative CL boulders at Rapaki and Purau sites exhibit typical elongate and flat morphologies.
Purau
Pre-CES and CES rockfalls are widely distributed at the Purau study location
(Fig. 3). Rockfall boulders are deposited on interfluves but are
predominantly concentrated within nearby canyons, highlighting the strong
influence of topography at the site (Fig. 3). Seven CES detachment zones
were identified in the field. CES rockfall boulders nearest to the Purau
village display the longest runout distance (372 m) and most distinct
spatial contrast with similarly sourced pre-CES boulders (deposited within
∼105 m of the local volcanic source rock) (Fig. 3a). Elsewhere, pre-CES boulders can be observed at further distances from the source rock than CES rockfalls. The ratio of pre-CES to CES rockfall boulders is ∼5:1 (Fig. 3a). Pre-CES VB boulders are deposited throughout the Purau location, while the deposition of CL pre-CES boulders is concentrated within the central and southern drainage canyons (Fig. 6a). The ratio of pre-CES VB to CL boulders is ∼2:1 (Fig. 3b). CES VB boulders (n=127) significantly outnumber CL boulders (n=9) at the Purau site (Fig. 3c), reflecting the lack of detachment within CL source rock lithologies during the CES. The ratio of CES VB to CL rockfall boulders is ∼14:1 and represents a significance difference compared with the corresponding pre-CES VB : CL ratio (Fig. 3c).
Boulder morphology and other characteristics
VB boulders (Fig. 4a–f) contain small to large porphyritic volcanic clasts
that exhibit minor to moderate vesicularity (up to ∼10 %)
and are embedded within a finer crystalline and ash-bearing matrix (see Fig. 4a, c, d and f). They are dominated by equant (all axes equal length) shapes (see Fig. 4c), although elongate (two short axes, one long) forms are observed. Flat (one short, two long axes) morphologies are rare. VB pre-CES boulder surfaces show a high degree of weathering and surface roughness
(Fig. 4a–d and f). The surface roughness results from in situ differential weathering between the finer crystalline host matrix and more resistant embedded volcanic clasts (see Fig. 4d). Surfaces show deep pitting, with amplitudes often exceeding 5–10 cm in height. CL boulders (Fig. 4g–k) are more texturally homogenous, contain fewer vesicles (estimated ∼<1 %), and exhibit a higher relative density (Carey et al., 2014; Muktar, 2014). The pre-CES CL boulder surfaces exhibit low surface roughness (i.e., smooth compared with VB boulders). Elongate and flat boulder morphologies predominate for CL boulder lithologies (Fig. 4g–k).
Both VB and CL pre-CES boulders can be observed partially to nearly
completely buried by loess colluvium (see Fig. 4a, b, g). Instances do occur,
however, where no sediment is built up at the boulder backside (Fig. 4c) due
to erosion (including tunnel gully formation). Burial in hillslope sediment
is most common for boulders located on midslope and footslope positions,
rather than those located on upper slope elevations, where erosion
dominates. Pre-CES boulders located in drainage canyons are subject to rapid
deposition and erosion, and therefore can be found without any sediment
pileup or preserving large colluvial wedges. VB boulders preserve the
thickest colluvial wedge sediments (see Fig. 4b).
Source rock characteristics
The volcanic source rock at Rapaki (Fig. 5a–c) and Purau (Fig. 5d and e) is
comprised of interlayered VB and CL layers (Fig. 5a–e). The breccia layers
comprise the bottom and top of discrete lava flows, while the coherent lava
generally occupies the center of the lava flow where cooling was not as
rapid, and there was less interaction with the substrate and/or cooling
interface (Fig. 5c–g). Jointing is pervasive within the volcanic source
rock, but to varying degrees depending upon layer composition and
corresponding texture. Layers comprised of CL exhibit the highest fracture
density (Fig. 5e and f) and were formed during primary cooling of the lava flow, producing a columnar-style pattern. The CL layers contain numerous
intersecting sub-vertical to vertical, to curvilinear joint sets, with
spacing rarely exceeding ∼1–2 m. The small joint spacing imparts a first-order control on CL boulder size and is reflected in the small size range for pre-CES CL boulders. Layers comprised of VB exhibit a lower fracture density, with joints more widely spaced (and irregular in shape), often 5–10 m or greater apart (Fig. 5d and e). The wider spacing for joints within VB layers promotes greater rockfall boulder volume (see Sect. 4.4. below).
(a) Volcanic source rock at Rapaki study site. Sixty individual detachment zones were created during the CES (yellow) and represent ∼9 % of the total source rock area. The source rock is
comprised of ∼86 % VB and ∼14 % CL. Approximately ∼69 % and ∼31 % of the detachments occurred within the VB and CL lithologies, respectively. (b) Photo showing several irregularly shaped CES detachment zones near the top of Mount Rapaki. (c) Photo showing freshly exposed VB and CL layering within the Rapaki source rock. (d) Portion of volcanic source rock at Purau showing VB and CL layering. A single CES detachment site is shown at the top of the source
rock. Seven individual CES detachment sites were identified at the Purau
study site. (e) CL and VB layers at the Purau study site. Note the thickness of the CL layer (∼5–7 m) and lack of any CES detachment
sites despite the high degree of fracturing and overhanging condition. (f) VB and CL layering in Sumner (Christchurch) cliff exposure adjacent to Main Road. Extensive cliff collapse during the CES has revealed multiple lava flows and the distinctive textural differences between the VB and CL lithologies. Note the high density of vertical to subvertical fractures within the CL layers. (g) Exposed lava layers adjacent to Main Road in Redcliffs (Christchurch). Note the single-family living residence at top of photo.
Relative locations of stations LPCC, D13C, D15C, and GODS (yellow
squares). Also shown are epicenters of the 22 February 2011 Mw=6.2 and 13 June 2011 Mw=6 earthquakes (yellow stars) along with Rapaki and Purau sites.
Each panel shows seismic data from LPCC (a, b), D13C (c), D15C (d), and GODS (e) stations. (a) and (b) compare ground motion, respectively, for 22 February 2011 Mw=6.2 and 13 June 2011 Mw=6 earthquakes at LPCC station. The left column shows east and north components of the velocity seismogram (blue line) and their respective envelopes (red dashed line). The particle velocity hodogram (middle column, green line) was determined for a time window ±5 s (shaded region in the left column) around the peak (red circle) of the east component envelope. The strike of the rock face (black short line segments) and the direction of the free face (red arrows) for sites PD1–PD4 and RAP are also illustrated. The particle
motion hodogram (gray line) is presented in the right column, where green,
yellow, and red segments represent, respectively, time points at which the east
component, the north component, or both components exceed an acceleration of
0.3 g. Note that scale of figure axes varies by station particularly for
ground motion.
During the CES, rockfall detachment occurred within approximately 9 % (by
area) of the volcanic source rock overlying the Rapaki study hillslope (Fig. 5a). The volcanic source rock is comprised of 86 % VB and 14 % CL (VB : CL ratio =∼6:1). Approximately 69 % of the CES detachment areas occurred within VB and the remaining 31 % within CL (Fig. 5a). However, 20 % of the identified CL source rock detached during the CES, while only 7 % of the identified VB source rock detached during the CES, indicating the CL lithology was more susceptible to detachment.
We were unable to conduct a source rock investigation at Purau with the same
spatial resolution as Rapaki because we considered the areal extent of the
bedrock source cliffs to be too large at Purau to address in this study and
there were safety concerns relating to access and potential for further
rockfalls. However, some observations were made for the Purau source rock
(Fig. 5d and e) as well as other volcanic coastal cliff outcrops at Sumner (Fig. 5f) and Redcliffs (Fig. 5g). Field observations indicate that CL layers at Purau are not as prevalent as (and generally thinner than) VB layers, but in some cases may exceed a thickness of 5 m, which is thicker than CL layers observed at Rapaki (see Fig. 5b and c). At Sumner and Redcliffs, VB and CL layers display roughly equivalent thicknesses (∼2–3 m), a condition not apparent at Rapaki or Purau. The variability in layer thickness presumably reflects differences in proximity to source vents and differing conditions during primary cooling of the lava flows.
Boulder volume
The size and frequency–volume distributions for pre-CES and CES rockfall
boulders (for volume ≥ 1.0 m3) at Rapaki and Purau display
similarity (Fig. 8a and c) and can be modeled using power law functions (Fig. 8b and d), with the number of rockfall boulders decreasing significantly as volume increases. Overall, statistical coherence is observed at the 25th, median, and 75th percentile boulder sizes; however, pre-CES
rockfalls are consistently higher for each of the size categories at the two
study locations (Table 1). Rapaki displays the highest pre-CES to CES
variance for 25th, median, and 75th percentiles, while Purau records
the biggest pre-CES to CES variance for the average, 95th percentile,
and maximum boulder volumes (Table 1, Fig. 8a and c). An inter-site comparison of rockfall volumes indicates that pre-CES rockfalls at Rapaki are greater for the 25th, median, and 75th percentile sizes (Table 1) while
Purau exhibits larger sizes for the 95th percentile, maximum, and mean
boulder categories (Table 1). For CES boulders, the 25th, median,
75th, and 95th percentile Rapaki CES boulders are slightly larger
compared with Purau CES boulders, while the maximum and mean boulder size
categories are higher at Purau (Table 1). Although differences are evident,
the overall size distributions are comparable (Table 1).
(a) Rockfall size distribution as a proportion of boulders less than a given size plotted in log space for CES and pre-CES rockfalls at Rapaki. (b) Rockfall frequency and size distribution for CES and pre-CES rockfalls at Rapaki. (c) Rockfall size distribution as a proportion of boulders less than a given size plotted in log space for CES and pre-CES rockfalls at Purau. (d) Rockfall frequency and size distribution for CES and pre-CES rockfalls at Purau. (e) Comparison of boulder size distributions for CES and pre-CES VB and CL rockfalls at Rapaki study site. (f) Comparison of boulder size distributions for CES and pre-CES VB and CL rockfalls at Purau.
Volumetric comparison of pre-CES and CES rockfall boulders (for
volume ≥ 1.0 m3) at Rapaki and Purau study sites.
The volume for pre-CES and CES VB boulders is significantly larger than the
corresponding CL boulders at Rapaki (Fig. 8e, Table 2) and Purau (Fig. 8f,
Table 2). At Rapaki, pre-CES VB boulders display higher volumes (compared
with CES VB boulders) in each of the size categories, particularly for
median and maximum boulder sizes (Table 2). Pre-CES CL boulders display
consistently higher values for each of the size categories with the
exception of the 75th percentile (Fig. 8e, Table 2). At Purau, CES VB and CL boulders exhibit a smaller distribution of boulder sizes compared
with their pre-CES equivalents (see Fig. 8f). Pre-CES VB and CL boulders are
higher in each of the size categories (Table 2, Fig. 8f), with the exception
of the median boulder size, where the CES CL median boulder volume is
slightly more than the pre-CES CL value (Table 2). It is notable that the
highest percent (%) variance in boulder volume between pre-CES and CES
boulders is recorded for the Purau VB boulders (Table 2); the only exception
is for maximum boulder size, where the percent (%) difference between
Purau CL pre-CES and CES boulders is even greater (Table 2).
Comparison of boulder size statistics for Rapaki and Purau VB and
CL pre-CES and CES rockfall boulders (volume ≥ 1.0 m3).
Rapaki Purau Pre-CESCESPre-CESCESPre-CESCESPre-CESCESVB (n=391)VB (n=45)CL (n=18)CL (n=3)VB (n=436)VB (n=127)CL (n=248)CL (n=9)(m3)(m3)(m3)(m3)(m3)(m3)(m3)(m3)25th (Q1)1.681.391.221.031.701.361.201.13Median3.12.211.381.063.212.041.561.6875th (Q3)6.785.71.541.677.654.872.302.1495th21.2820.5763.922.1640.9117.785.262.48Maximum200.5628.359.992.28616.0079.9726.212.64Mean7.035.061.961.4511.435.582.241.67Total volume2749.07227.8035.294.344938.76708.34555.6315.00% of total volume9998128998112% of mapped boulders9694466493367
The volume and frequency ratios for pre-CES and CES rockfall boulders are
plotted in Fig. 9a. The pre-CES to CES boulder volume ratios at Rapaki and
Purau range from ∼8–12 and ∼7–37, respectively (Table 3a, Fig. 9a). The corresponding frequency ratios are consistently lower, ranging from ∼6 to 8.5 and ∼3.5 to 27.5 (Table 3a, Fig. 9a). Overall, the boulder volume and frequency ratios are greater at Rapaki, with the exception of the CL lithology (Tables 3a and b, and Fig. 9a).
(a) Frequency ratio versus volume ratio for pre-CES and CES rockfall boulders. (b) Frequency–runout distributions for Rapaki pre-CES and CES boulders. Both power law (without extrapolated data) and exponential (all data) fits are shown for the prehistoric boulder data set. A poor exponential fit is shown for CES rockfalls. (c) Plot of travel distance on talus slope (Lt) versus height on talus slope (Ht) with fitted polynomial regression lines for pre-CES and CES rockfalls at Rapaki. (d) Plot of Lt
versus Ht with fitted linear, log, and polynomial regression lines for pre-CES and CES rockfalls at Purau. Four separated domains (here D1–D4) are defined at Purau to evaluate the shadow angle method. (e) Plot of rockfall size (m3) versus tangent of the shadow angle (Ht/Lt) for Rapaki rockfalls. No tendency of the data is evident. (f) Plot of rockfall size (m3) versus tangent of the shadow angle (Ht/Lt) for Purau rockfalls. The tendency for the domain data sets is poor. Values of correlation coefficients are below 0.3.
(a) Comparison of frequency (n) and volume (m3) ratios for pre-CES and CES rockfall boulders at the Rapaki and Purau study sites. (b) Comparison of VB / CL frequency (n) and volume (m3) ratios for pre-CES and CES rockfall boulders at the Rapaki and Purau study sites.
(a)No. of pre-CES rockfalls :Pre-CES : CESPre-CES : CESVolume of pre-CES rockfalls :Pre-CES : CESPre-CES : CESNo. of CES rockfallsratio% : %volume of CES rockfallsratio% : %(n)(m3)Total (Rapaki + Purau)1093:1845.9486:148323.76:955.488.7190:10Rapaki total409:488.5289:112784.37:232.1411.9992:8Rapaki VB391:458.6990:102749.07:227.8012.0792:8Rapaki CL18:36.0086:1435.29:4.348.1489:11Purau total684:1365.0383:175539.39:723.357.6688:12Purau VB436:1273.4377:234983.76:708.347.0488:12Purau CL248:927.5696:4555.63:15.0037.0497:3(b)No. of VB boulders :VB : CLVB : CLVolume of VB boulders :VB : CLVB : CLNo. of CL bouldersratio% : %volume of CL bouldersratio% : %n:nm3: m3Total (Rap + Purau)999:2783.5978:228668.97:610.2614.2193:7Rapaki Total (pre-CES + CES)436:2120.7695:5976.87:39.6375.1199:1Rapaki pre-CES391:1821.7296:42749.07:35.2977.999:1Rapaki CES45:31594:6227.80:4.3452.4998:2Purau Total (pre-CES + CES)563:2572.1969:315692.1:570.639.9891:9Purau pre-CES436:2481.7664:364983.76:555.638.9790:10Purau CES127:91493:7708.34:15.0047.2298:2Purau D1 pre-CES17:0not applicable100:0137.27:0not applicable100:0Purau D1 CES30:0not applicable100:0125.86:0not applicable100:0Purau D2 pre-CES36:31292:8230.8:3.959.1898:2Purau D2 CES1:1150:5014.78:1.0813.6993:7Purau D3 pre-CES54:431.2656:44203.79:142.621.4359:41Purau D3 CES38:312.6793:7242.63:5.9141.0598:2Purau D4 pre-CES8:1889:11188.42:1.24151.9599:1Purau D4 CES36:0not applicable100:0267.76:0not applicable100:0
The calculation of VB and CL boulder percentages at Rapaki for pre-CES and
CES rockfalls indicates that VB boulders comprise ≥ 98 % by volume
and ≥94 % by frequency (n) for all Rapaki conditions, while at Purau
the corresponding percentages are ≥90 % (volume) and ≥64 %
(frequency), respectively (Table 3b). All of the lowest VB percentages exist
at the Purau study location (see Table 3b, individual domain data).
Boulder runout distance
The frequency–runout distance distribution for pre-CES boulders at Rapaki
can be characterized by power and exponential laws (Fig. 9b), with the
number of rockfall boulders with long runout distances decreasing
dramatically with increasing distance from the volcanic source rock. The
exponential regression is best fit to the entire data set (including
extrapolated boulders within 100 m of source rock), while the power law
displays the strongest fit for the mapped rockfall boulders (Fig. 9b). CES
rockfalls display a poor exponential fit and do not indicate a similar
inverse relationship between boulder frequency and runout distance (Fig. 9b). The frequency–runout distribution for CES rockfalls indicates that the
number of boulders remains more or less consistent regardless of distance
from the source rock. Using the shadow angle method, we plot travel distance
on the talus slope (Lt) versus height on the talus slope (Ht) with a fitted
polynomial regression line (Fig. 9c). The correlation coefficient is
0.9699 for CES rockfalls and 0.9717 for pre-CES rockfalls (Fig. 9c). The minimum shadow angle for pre-CES is 25∘, while the minimum shadow angle (for the furthest traveled CES rockfall boulders) is 23∘. At
Rapaki, the maximum runout distance for pre-CES and CES VB boulders exceeds
the furthest travel distances for pre-CES and CES CL boulders, respectively
(Table 4). The CES VB boulders exceed pre-CES VB runout by ∼165 m and CES CL boulders exceed CL pre-CES runout by ∼138 m (Fig. 2a and b; Table 4).
Average and maximum runout distances for pre-CES and CES rockfall
boulders (for volume ≥ 1.0 m3) at Rapaki and Purau study sites.
RunoutAverageMaximumdistance(m)(m)(MLR)Rapaki Pre-CES184.30567.51CES276.23702.47Pre-CES VB184.65567.51Pre-CES CL176.57346.73CES VB276.91702.47CES CL266.13432.14Purau PD1 Pre-CES29.8696.96PD1 CES119.63348.4PD2 Pre-CES84.01279.75PD2 CES14.1115.91PD3 Pre-CES239.62462.8PD3 CES237.24413.35PD4 Pre-CES109.11208.85PD4 CES181.75304.56PD1 Pre-CES VB29.8696.96PD1 CES VB119.63348.4PD1 Pre-CES CLnot applicablenot applicablePD1 CES CLnot applicablenot applicablePD2 Pre-CES VB88.73279.75PD2 CES VB12.312.3PD2 Pre-CES CL27.3933.38PD2 CES CL15.9115.91PD3 Pre-CES VB248.96434.85PD3 CES VB243.21413.35PD3 Pre-CES CL227.89462.8PD3 CES CL161.68178.53PD4 Pre-CES VB106.99208.85PD4 CES VB181.75304.56PD4 Pre-CES CL126.06126.06PD4 CES CLnot applicablenot applicable
MLR : Map length runout and PD1 : Purau Domain 1.
At Purau, Lt versus Ht is plotted for four separate geomorphic domains (PD1–PD4) to evaluate the distribution of pre-CES and CES boulder runout distances (Fig. 9d; see Fig. 3 for domain locations). The pre-CES and CES rockfalls for the individual domain data sets are characterized by a variety of regression functions with high correlation coefficients (Fig. 9d; S24 in the Supplement). CES rockfalls in PD1 and PD4 have significantly further maximum runout distances than their pre-CES counterparts, while the inverse is evident in PD2 and PD3. (We note that only two CES boulders were observed in PD2.) The minimum shadow angle for pre-CES rockfalls at Purau is 25∘, while the corresponding minimum CES rockfall shadow angle is 18∘. At Purau, the longest recorded runout distances occur for pre-CES CL and VB boulders and CES VB rockfall boulders within PD3 (Table 4).
At Rapaki, no relationship has been obtained plotting individual boulder
volumes and the tangent of the shadow angle (Fig. 9e). A wide range of
boulder sizes are evident for the full spectrum of pre-CES and CES rockfall
runout distances by means of the shadow angle. The same is largely true at
Purau, where correlations for the individual domains (PD1–PD4) are poor and
the data have a high degree of scatter (i.e., low correlation coefficients);
although the data do show a slight negative relationship between block
volume and Ht/Lt ratio value (that is, a slight increase in runout distance as boulder size increases) (Fig. 9f).
RAMMS rockfall modelingRAMMS_1
Final emplacement locations (Q95%) are generated for simulated rockfalls released from the seven field-identified CES detachment zones at Purau (labeled CES-1 through CES-7) (Fig. 10a). Observed CES boulder locations are depicted as red circles. RAMMS_1 (bare-earth CES model
scenario) is successful in replicating the overall spatial pattern for
detached and distributed CES rockfalls at Purau for locations CES-3–7. Below the CES-7 source rock, RAMMS maximum runout distances (∼370 m) are well matched to the maximum travel distance for mapped CES rockfalls (∼357 m). Maximum runout distances for the RAMMS boulders are overestimated at CES-1 and CES-2 (Fig. 10a). We note that only two boulders were released at CES-1 during the CES and were deposited within ∼12 m of the source rock. RAMMS_1 effectively captures the lateral dispersion for the mapped CES boulders at CES-2–CES-4, but overestimates this effect within the CES-5 and CES-6 valleys, and slightly underestimates the lateral dispersion of CES rockfalls beneath CES-7.
(a) RAMMS_1 shows deposited rocks for simulated CES
boulders. Mapped CES boulders (red circles) are shown for comparison. Boulder densities of 2500 and 3000 kg m-3 are used for VB and CL boulders, respectively. (b) Final resting locations for RAMMS_2 rockfalls. RAMMS_2 assumes prehistoric rockfall conditions (i.e., forested hillslope). Mapped prehistoric rockfalls are depicted (yellow circles) for comparison. An increase in forest density to 10 000 kg s-1 generates the best fit with maximum runout distance (see white dashed line) for mapped prehistoric boulders. (c) Final resting locations for RAMMS_3 boulders. RAMMS_3 assumes modern hillslope conditions (i.e., deforested hillslope). Note the increased maximum runout distance for RAMMS_3 boulders compared with RAMMS_2 and the potential future rockfall hazard to development sites S1 and S2. The provided development sites are modified from Eliot Sinclair and Partners Ltd. (2013). (All images are modified after Land Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
RAMMS_2
The RAMMS_2 model scenario (forested hillslope) is moderately successful (slight overprediction) in replicating the overall spatial distribution and maximum runout distances for the majority of mapped pre-CES rockfalls at Purau (Fig. 10b). The exception is area CES-7, where RAMMS predicts deposition of pre-CES boulders significantly farther (∼325 m) from the source rock than is evident in the field (∼80 m). Elsewhere, the greatest variance in maximum runout distance between RAMMS_2 and the mapped pre-CES boulders is ∼75–100 m (see Fig. 10b). An increase in forest density to 10 000 kg s-1, spread uniformly across the study site, produces the best fit to the pre-CES boulder spatial distributions (in particular, maximum runout distance) (see Fig. 10b, white dashed line). RAMMS_2 successfully models the lateral dispersion for the mapped pre-CES boulders (with the exception of area CES-7) (Fig. 10b). The RAMMS_2 model scenarios identify pre-CES rockfall boulders that have likely
experienced post-emplacement mobility (see Fig. 10b). Note the collection of
pre-CES boulders within the central drainage canyon that exceeds the limit of
simulated RAMMS boulders (Fig. 10b). Field observations confirm that boulder
depositional patterns beyond the limits of the final resting locations for
RAMMS simulated rockfall boulders are consistent with deposition by debris
flow and other transport or deposition processes. This is further highlighted
by the numerous and large pre-CES rafted boulders (maximum volume = 20 m3) identified near the Purau coastline (see Fig. 3). Finally, we observe no mapped pre-CES boulders outside of the valleys that exceed the RAMMS_2 simulated maximum runout distances.
RAMMS_3
RAMMS_3 models the potential future rockfall hazard at Purau and assumes a bare-earth (deforested) hillslope and dry soil moisture conditions to insure a worst-case (conservative) outcome (Fig. 10c). As expected, RAMMS_3 rockfalls obtain higher kinetic energy, velocity, and jump heights than RAMMS_2 boulders (see S18 and S19 in the Supplement), and as a result, runout is farther than that of the RAMMS_2 boulders (Fig. 10b). On average, maximum runout distance for RAMMS_3 boulders is ∼450–500 m, representing an increase of ∼100–150 m compared with RAMMS_2 boulders, a difference consistent with results from RAMMS numerical modeling at Rapaki (see Borella et al., 2016a). With the exception of area CES-7, RAMMS_3 maximum runout distances are well in exceedance of the mapped locations for the CES rockfall boulders (Fig. 10a and c).
Strong ground motion data
High-frequency data show complex velocity and displacement paths for any
given site. The variations across the sites are significant, as reported
previously (Van Houtte et al., 2012; Bradley, 2016). At the same site (LPCC,
Fig. 7a and b), particle velocity and motion hodograms show different
polarization characteristics for different earthquakes. Peak velocities and
displacements recorded at LPCC site are higher for the Mw=6.2 than the smaller event Mw=6.0 (Fig. 7a and b). The observed inter-site and inter-event variations in polarization of peak velocities and displacements can be attributed to source radiation pattern (Lee, 2017) and complex wave propagation effects such as scattering. For instance, simulating high-frequency (>1 Hz) 3-D wavefields, Takemura et al. (2015) showed
that near-station irregular topography amplifies scattering of seismic
wavefield, producing long coda and distortions to P wave polarizations. This is not surprising given that Fresnel volume – the region to which a
transmitting seismic wave is sensitive – is inversely related to wave
frequency (Spetzler and Snieder, 2004), due to which near-station geological
conditions modify wave characteristics at high frequencies. The control of
near-station geology over polarization and amplification characteristics at
high frequencies (Bouchon and Barker, 1996) reduces our ability to
extrapolate these characteristics to distant sites.
DiscussionRockfall spatial distributions and frequencies
At Rapaki, significant differences in the spatial distribution of
pre-CES and CES boulder populations are observed (Fig. 2 and Table 4). The
increased distance for the CES rockfall boulders is interpreted as an effect
of anthropogenic deforestation on the hosting hillslope, which enabled CES
boulders to travel further than their pre-CES counterparts due to reduced
resistance from vegetation (Borella et al., 2016a). The increase in CES
runout distance (∼165±15 m) and corresponding reduction in minimum shadow angle resulted in significant impact and damage to homes and infrastructure in the Rapaki village, highlighting the importance of considering the effects that modifications to hillslopes may have on rockfall hazard. At Rapaki, pre-CES VB boulders are present in significantly greater number and have further average and maximum runout distances than the pre-CES CL boulder lithologies (Fig. 2a, Table 4). A similar relationship is evident between the CES VB and CL boulders, where CES boulders with the furthest runout distances are exclusively comprised of volcanic breccia (Fig. 2b). It is possible that the reduced runout distances for pre-CES and CES CL boulders are a statistical counting bias (i.e., low number of CL boulders for
volume ≥ 1.0 m3), but a more plausible explanation is that the reduced runout distance for CL boulder lithologies is a result of CL boulder shapes being dominated by elongate and flat morphologies (Fig. 4g–k), which would have more difficulty traveling downslope.
At Purau, discerning the differences in spatial distribution between pre-CES
and CES rockfalls is more difficult, primarily due to the topographic
forcing of rockfalls into nearby drainage valleys and post-emplacement
mobilization (Fig. 3). The CES-7 site location (furthest southern rockfalls) shows a similar pre-CES : CES spatial scenario to Rapaki, with CES boulders
traveling significantly further than their pre-CES equivalents (see Fig. 5);
a discrepancy which could also be attributed to intervening deforestation on
the hillslope. However, elsewhere at the Purau field site inverse spatial
scenarios are evident, with pre-CES boulders deposited further from the
source rock than their CES counterparts (see Fig. 2a, Table 4). This is
primarily observed within drainage valleys where field observations suggest
pre-CES boulders have been remobilized (debris flows, floods) and carried
further from the source rock following their initial emplacement.
The CES rockfall boulders at both sites represent a subset of the larger
pre-CES rockfall database, suggesting the preservation of multiple pre-CES
rockfall events. The ratio for the number of pre-CES to CES rockfall
boulders is higher at Rapaki (∼8.5:1) than Purau (∼5:1) (Table 3, Figs. 2 and 3). One cause of the observed difference may be the higher number of CL boulders with size ≥ 1.0 m3 at the Purau study site (Fig. 8e and f). At Rapaki, most of the detachment within the CL source rock generated boulder volumes below the 1.0 m3 threshold. As a result, the ratio of pre-CES VB : CL boulders is significantly higher at Rapaki (∼22:1) (Table 3b, Fig. 2a) than Purau (∼2:1) (Table 3b, Fig. 3b). This contrasts with the ratio of CES VB : CL boulders at Rapaki (∼15:1) (Table 3b, Fig. 2b) which shows near equivalence to Purau (∼14:1) (Fig. 3c). The CES VB : CL ratio at Purau is more consistent with our field observations where VB predominates in the source rock. Overall, the results indicate there is a high degree of variability for lithology and discontinuity spacing (e.g., joints) within the source rock and suggests the cumulative ratio of VB : CL boulders can be significantly different from that generated locally during a single rockfall event.
Boulder morphology and other characteristics
The shapes for the VB (Fig. 4a–e) and CL (Fig. 4g–k) boulders are primarily
controlled by pre-existing discontinuities (primarily joints) in the source
rock. We modeled the influence of boulder shape on spatial distribution for
the VB and CL lithologies assuming detachment from the CES-7 site (under
bare-earth conditions) using RAMMS (Fig. 11). To eliminate the effect of
boulder size, a volume of 1.0 m3 was assumed for all rockfall boulders.
The VB boulders were assigned a range of equant boulder shapes, while CL boulders were assigned only elongate and flat boulder morphologies. The
model results highlight the differences in boulder spatial distribution
resulting from differences in boulder shape, with equant (VB) boulder
lithologies displaying a significantly higher relative percentage of longer
runout distances (Fig. 11a) compared with the elongate/flat (CL) boulder
morphologies (Fig. 11b). We recognize that the modeling represents an ideal
scenario (i.e., other transition morphologies do exist for the VB and CL boulders) and was conducted primarily to provide a sense for the expected
spatial patterns assuming the distinct VB and CL boulder shapes. Further
work is required to verify coherence between field observations and model
results.
RAMMS simulated rockfall boulders showing differences in spatial
distribution between VB (mostly equant shaped) and CL (predominantly
elongate and flat shaped) boulder morphologies at Purau. All simulated
boulders assume a volume of 1.0 m3. (a) Spatial distribution of simulated VB boulders at Purau CES-7 location. Note the high relative
percentage of simulated boulders deposited at the base of the hillslope
(∼500–600 m from source rock). (b) Spatial distribution of simulated CL boulders at CES-7 location. Note the higher relative percentage of rockfall boulders deposited near the source rock (within ∼100 m from source rock). The simulation highlights the strong influence of boulder shape on runout distance. (All images are modified after Land Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
Source rock characteristics
The VB and CL percentages in the Rapaki source rock (86 % VB and 14 % CL) are lower than the corresponding VB and CL percentages determined from
rockfall frequency and volume for the pre-CES (96 % VB and 4 % CL) and
CES (94 % VB and 6 % CL) rockfalls. We attribute the percent differences
between source rock and rockfalls to the influence of the larger VB boulder
sizes and the lower number of CL rockfalls meeting the ≥1.0 m3
size threshold. These two factors also explain detachment during the CES,
where 69 % of the detachment areas occurred within VB and the remaining
31 % within CL (Fig. 5a–c), yielding a lower VB : CL ratio of ∼2:1 compared with the corresponding boulder volume and frequency ratios (∼15:1 and ∼52:1, respectively) (Table 3b).
Boulder volume
The size and frequency–volume distributions for pre-CES and CES rockfalls at
the two study sites can be modeled using a power law (Fig. 8a–d): a
relationship that is well-established (e.g., Dussauge-Peisser et al., 2002;
Guzzetti et al., 2002) for rockfalls globally and has also been successfully
applied for CES rockfalls in Banks Peninsula (Massey et al., 2014). The net
increase in volume distribution for pre-CES boulders could represent a
statistical effect and reflect the inclusion of more boulders into the
rockfall data set through time (which would increase the likelihood of larger boulders) and/or could reflect higher shaking intensities and/or
source rock vulnerability during pre-CES events. Variations in CES vs. pre-CES boulder volumetric distributions for the same lithologies could
reflect structural and/or more subtle lithologic variability within the
source cliffs from which boulders were derived, and/or post-detachment
weathering during boulder transport or in situ. The significantly higher volumes for VB boulders (pre-CES and CES) at both study sites reflects the predominance of VB within the source rock and wider joint spacing within the thicker VB layers.
Boulder runout distance
The exponential law fit for pre-CES boulders (Fig. 9b, short dashed blue
line) highlights the importance of slope and initial impact velocity at the
cliff base, which causes more boulders to be deposited at greater distances
and creates a deviation from the power law fit (Fig. 9b, solid blue line).
The exponential fit for CES rockfall boulders is poor and indicates there is
no discernable correlation between CES boulder frequency and runout distance
(Fig. 9b, solid red line). Despite the low number of CES boulders (n=48),
it is interesting that the CES runout distribution shows such a noticeable
deviation from the pre-CES data set and could reflect the influence of
deforestation on runout distance. This would imply that the incremental
input of CES and future rockfalls at Rapaki (emplaced during bare-earth
conditions) will modify the overall trend for the cumulative rockfall data
set.
At Rapaki, the shadow-angle Ht/Lt relationship is fit best using a polynomial regression (Fig. 9c). The trend indicates a positive correlation between talus slope height (Ht) and travel distance on the talus slope (Lt), with a reduction in the rate of increase as rockfall runout (Lt) increases. At Purau, CES and pre-CES rockfalls (within individual geomorphic domains) are modeled using a variety of data functions (e.g., linear, log, and polynomial), suggesting intra-site geomorphic and geologic factors affecting rockfall hazard are spatially variable (Fig. 9d). We note that Copons et al. (2009) reports linear regression lines for historical rockfalls in the Central Pyrenees using the shadow-angle method, and locally Massey et al. (2014) also show linear regression fits using the shadow-angle method for CES rockfalls in the Port Hills of southern Christchurch. Our data indicate that non-linear regression functions (for the shadow-angle method) are more successful in capturing the Ht/Lt relationship as distance from the source rock increases. At both sites, a wide range of boulder sizes exist for the full spectrum of pre-CES and CES Ht/Lt ratios, suggesting that boulder size is not a primary driver for runout distance at the study sites; although it is possible that smaller boulders (e.g., ∼1–2 m3) exhibiting long runout distances (i.e., low Ht/Lt ratios) may represent smaller rock fragments detached from larger boulders during transport and eventual emplacement on the hillslopes and within valleys.
RAMMS rockfall modelingRAMMS_1
A primary challenge in replicating the distribution of CES rockfalls was
determining an appropriate set of terrain parameters for the drainage
valleys (see Table A1). To match the RAMMS boulders with the field-mapped CES rockfalls (Fig. 10a) it was necessary to create separate valley terrain polygons and modify the terrain parameters to reflect the high degree of impedance and/or dampening (Vick et al., 2019) in the drainage gullies (see Table A1). Our field observations confirm the presence of abundant pre-existing boulders within drainage valleys (Fig. 12a–f) and many instances where CES boulders were stopped by pre-CES rockfalls (see Fig. 12a–c). The effect of pre-CES rockfall debris on boulder transport and final resting location needs to be further investigated in order to effectively model impediments within drainage valleys. Further, a more refined understanding of the influence that substrate soil moisture content has on rockfall runout is required (Vick et al., 2019). We note that
the DEM used for our study has a resolution of 4 m and may not adequately
simulate the smaller scale surface roughness (e.g., clustering of boulders
below this size threshold) observed during our field studies (Fig. 12a–g).
CES and pre-CES rockfall boulders within drainage valleys at Rapaki (a, c) and Purau (b, d–f) study locations. Drainage valleys contain a high amount of pre-CES rockfall boulders, which impacts the trajectory or path of CES rockfalls and reduces or stops runout distance.
RAMMS_2
The best RAMMS_2 model fit occurs when the forest density is increased (to 10 000 kg s-1) and applied uniformly across the Purau hillslopes
(see Fig. 10b, white dashed line). This represents an increase compared
with the forest density used at Rapaki (i.e., 3000 kg s-1 for moderate
vegetation (interfluves), 6000 kg s-1 for dense vegetation (valleys) (see Borella et al., 2016a) and implies that vegetation may have been denser on the northwest-facing Purau hillslopes compared with the south-southeast-facing Rapaki hillslope.
We note the difference between maximum runout distance for RAMMS and
empirical pre-CES boulders at the CES-7 site (Fig. 10b). Several possible
explanations exist including the following: (1) pre-CES boulders were in fact deposited
further from the source rock and were subsequently buried by loess and
hillslope colluvium; (2) RAMMS underestimates the effect of hillslope
vegetation at Purau during prehistoric times; (3) during pre-CES times less
of the source rock was exposed (due to burial) and therefore the volcanic
rock was less susceptible to detachment during shaking; and/or (4) during
pre-CES shaking events the direction of strong ground motion was not
favorable to rockfall detachment. Scenario 1 is possible but would need to
be confirmed through subsurface trenching or ground penetrating radar (GPR)
methods. Tunnel gulley erosion has exposed sections of the subsurface on the
CES-7 hillslope and no buried boulders are evident. Scenario 2 is probable
based on our observations of forested hillslopes elsewhere in the Port Hills
and greater Banks Peninsula area. It is common for dense native vegetation
to grow up to, and in some cases, onto portions of the volcanic source rock.
In these cases, a high volume of detached rockfalls are stopped adjacent to
the source rock and never generate the required momentum to runout an
appreciable distance. Scenario 3 is also a possibility and requires that the
CES-7 source rock was partially buried during emplacement of the pre-CES
rockfalls. The last phase of hillslope aggradation would have occurred
during the last glacial maximum (∼18–24 ka) and possibly up
to ∼12–13 ka (see Borella et al., 2016b). We assume the Purau
hillslopes have been net erosional (i.e., downwasting) since the early
Holocene; a condition that would have been significantly accelerated after
deforestation in the Purau area. Scenario 4 is a final possibility but would
require that the ∼ north facing PD1 source rock is oriented in
such a way that strong ground motions from multiple prehistoric shaking
events were unable to create rockfall detachment to the degree evident in
the CES (see Sect. 5.7 for more discussion on strong ground motions).
RAMMS_2 model scenarios effectively identify pre-CES rockfall
boulders that have likely experienced post-emplacement mobility (Fig. 10b).
This is shown by the collection of pre-CES boulders within the central
drainage canyon that exceed the limit of simulated RAMMS boulders (Fig. 10b), indicating a transport mechanism other than rockfall. This result has
implications for rockfall hazard studies because boulder locations not
reflective of cliff detachment and subsequent downslope displacement by
bouncing, sliding, and rolling (that is, rockfall) should be excluded from
any data set before assessing the potential rockfall hazard and associated
risk. Furthermore, paleoseismic studies attempting to determine the timing
and recurrence interval of prehistoric rockfall events should avoid using
boulders with complex post-emplacement mobility histories.
The absence of any pre-CES boulders exceeding the RAMMS_2 maximum runout distance (with the exception of rockfalls within valleys) (Fig. 10b) implies that the mapped pre-existing boulders were deposited prior to deforestation of the Purau hillslopes and are prehistoric (i.e., deposited prior to European arrival) in age. This result is consistent with prehistoric boulder ages determined at the Rapaki study site where the youngest emplacement ages for pre-CES boulders are ∼2–6 ka (Mackey and Quigley, 2014; Borella et al., 2016b).
RAMMS_3
RAMMS_3 highlights the increased spatial extent (including maximum runout distance) of rockfalls that could result from more widespread detachment within the Purau source rock, particularly for detachment sites
overlying hillslopes where boulder trajectories are not as strongly
influenced (i.e., captured) by nearby valleys. Although we caution against
using RAMMS_3 as a rockfall hazard map, the model results do
provide a first-order indicator of low-lying areas that are most susceptible
to future rockfall hazard and suggest that development at the S1 and S2 sites could be adversely impacted by future rockfall events (Fig. 10c).
Assuming terrain characteristics remain similar, sites 3–5 are
unlikely to be impacted by rockfall boulders in the future, although
additional mapping and related structural studies of the volcanic source
rock is required to determine the most vulnerable rockfall source areas.
Interpretations of strong ground motion data
Preceding studies provide some insight into possible strong ground motion
characteristics at Rapaki and Purau during the Mw=6.0 and 6.2 earthquakes. The study by Kaiser et al. (2014) provided seismic array analysis of weak ground motion provides information regarding frequency-dependent amplification at Kinsey Terrace, Redcliffs, and Mount Pleasant (henceforth Ksites), all of which are north-facing slopes in the Port Hills. They found that both morphological
features as well as properties of the wave propagation media control
frequency-dependent amplification. Significant ground motion amplification
was observed at 1–3 Hz frequency range on top of narrow, steep-sided
ridges. At these low frequencies (f), seismic wavelengths (λ) are
comparable to ridge width of Ksites. Therefore, seismic waves in the 1–3 Hz frequency band appear to excite natural resonance (or natural frequency;
fn), optimizing ground motion.
It is interesting to evaluate the implications of the low-frequency observations of Kaiser et al. (2014) to the Rapaki and Purau rockfall sites. Both these sites
are located at higher elevations than Ksites. Thus, their ridge width
(∼400–500 m) is somewhat less than that at Ksites (∼600–1000 m). Using this information, we estimate fn to be <5 Hz (see Supplement).
Whether ground motion with fn was excited at these sites depends on the amount of energy carried by seismic waves in that frequency band. This
information is contained in the spectra of velocity seismograms – a proxy
for kinetic energy distribution over frequency. We selected the D13C station for
this preliminary analysis because the distance between this station and the
Rapaki site is only about 2 km. They are also at similar elevations with
ridge morphologies resembling each other. Rapid variations in geological
conditions are unlikely over such short length scales, which allows us to
extrapolate both high- and low-frequency wave characteristics observed at
the D13C station to Rapaki with less uncertainty than the other stations. The
nearest station to Purau is LPCC (∼5 km). The two sites are
vastly different as LPCC is located at the toe of a steep cliff in the
Lyttelton Port, whereas Purau sites are high-elevation ridges. Thus, ground
motion recorded at LPCC is not a reliable proxy for ground motion
characteristics at Purau. The next nearest station, D15C, is ∼7 km from Purau and it suffers from morphological dissimilarities (variations
in ridgeline orientation and morphology) that make extrapolating ground
motion between the sites highly unreliable. Although the D13C station is
located ∼10 km from Purau, the similarity of morphological
features including elevation makes D13C a desirable station to understand
ground motion at Purau.
We computed velocity spectra of east and north components of the station D13C (Fig. 13) to qualitatively assess seismic energy transmission through
our rockfall sites. We find that the transition from the flat spectrum to a
rapid fall off occurs at ∼3–4 Hz. This means that the 13 June 2011
Mw=6 earthquake carried most of its energy at frequencies less
than ∼3–4 Hz. Together with our estimates of fn (<5 Hz), we can thus infer that the passage of seismic waves
excited natural resonance at the Rapaki and Purau sites. The combined effects of
natural resonance and wave focusing towards the ridge crest (Hartzell et
al., 1994; Bouchon and Barker, 1996) in these hard rock sites have the
potential to optimize shaking, promoting rockfalls.
Velocity spectra for the 13 June 2011 Mw=6 earthquake recorded at station D13C. No path corrections are applied.
It is interesting to note, however, that D13C recorded the lowest peak
velocities (223 and 178 mm s-1) and displacements (38 and 74 mm) of
the four stations considered here (Fig. 7c). Out of these stations, it is
also the only station that recorded no acceleration above 0.3 g on any
component. These features of the wavefield are not surprising because
distance from D13C to epicenter of the Mw=6 earthquake is twice
(∼9 km) as large as that from the other stations (∼4.5 km). For this reason, it is likely that other possible effects (e.g., rock mass weakening by prior CES earthquakes), in addition to strong ground motions from the Mw=6 earthquake, were responsible for triggering major rockfalls at the study sites. Unfortunately, the D13C station was not in operation at the time of these previous larger earthquakes to assess severity of ground motion. Nonetheless, records from stations closest to D13C indicate that those sites have exceeded the 0.3 g peak ground acceleration (PGA) threshold important for engineering considerations. For instance, LPCC station located ∼6 km from D13C recorded 0.3 and 0.9 g PGA following the Mw=7.1 and Mw=6.2 events respectively (Bradley
and Cubrinovski, 2011). Moreover, extrapolation of PGA contours of Bradley (2012) suggests that D13C and Rapaki sites experienced PGAs exceeding 0.25 and 0.45 g during Mw=7.1 and Mw=6.2 earthquakes respectively. Some of the rockfall sites investigated herein might have had reached a critical failure threshold prior to being triggered by the 13 June 2011 Mw=6 earthquake.
Particle velocity and motion hodograms (Fig. 7a–e) also carry directional
information of particle behavior in addition to intensity. Past studies show
that seismic wave polarizations are amplified in directions perpendicular to
fracture surfaces, weakening the coherence between outer blocks of rock with
bedrock during the passage of a seismic wave (Kleinbrod et al., 2017;
Burjánek et al., 2018). If blocks of rock are primed for failure by
previous events, this effect can produce rockfalls in earthquakes as small
as local magnitude 4.0 (Keefer, 1984). The velocity hodogram of D13C
exhibits a strong ENE–WSW component. Note that this direction makes roughly
∼30 to ∼60∘ angle with rock faces at PD2–PD4, and RAP sites (Fig. 7c). Thus, it is reasonable to assume that particle velocities in this dominant direction are favorable for triggering rockfalls particularly if the rock faces were primed for failure. The angle between this dominant velocity component and the rock face at PD1 site, however, appears to be less than ∼20∘ and possibly is not as favorable for triggering
rockfalls as for other sites. On the other hand, the particle motion
hodogram has two dominant directions: WNW and WSW. Depending on the strike
of the rock face, either one of these directions can orient particle motion
favorably for rockfalls. For instance, site RAP has a rock face strike of
25∘, which is sub-parallel to the WSW particle motion direction. However, the WNW particle motion direction makes a steep angle with the rock face and thus can promote rockfalls. Combining information from particle velocity and motion hodograms, we hypothesize that directional aspects were favorable to rockfall triggering at the Rapaki and Purau sites.
Pre-existing rockfalls as predictive database
Our study indicates that pre-existing rockfalls provide an accurate range of
expected boulder volumes, shapes, and % lithologic variance (i.e., VB vs. CL), but their use as a spatial indicator for future rockfalls should be
approached with caution because there are a variety of geologic and
anthropogenic factors that influence the final resting location for
rockfalls. These factors include changes to the rockfall source (i.e., emergence of bedrock sources from beneath sedimentary cover), remobilization of prior rockfalls by surface processes including debris flow transport, collisional impedance with pre-existing boulders, potential natural and human-induced landscape changes (including deforestation), and variations in the location, size, and strong ground motion characteristics of past rockfall-triggering earthquakes. Our study indicates that pre-CES rockfalls underestimated the expected average and maximum runout distances on
interfluves, in part, because pre-CES rockfalls were probably emplaced on a
forested hillslope. Conversely, the locations for pre-CES boulders in
well-established drainage valleys or channels may overestimate the expected
runout for future rockfalls because the rockfalls have been remobilized
after their initial emplacement.
Prior to the CES, rockfall hazard was not considered a major risk in Banks
Peninsula and surrounding areas (Townsend and Rosser, 2012), including the
Port Hills of southern Christchurch, where damage was most critical and five fatalities occurred (Massey et al., 2014). To date, we are aware of only
four studies that have dated pre-CES rockfalls in Banks Peninsula (Mackey
and Quigley, 2014; Borella et al., 2016b; Sohbati et al., 2016; Litchfield
et al., 2016), and all of these investigations were undertaken after the
CES. We assume this was primarily because there were few records of
historical rockfall occurrence, and of those described (Lundy, 1995), none hinted at the potential for future widespread cliff collapse and rockfall in the region. However, the geologic record (i.e., prehistoric rockfalls) provides evidence that rockfall events of similar magnitude (or greater) have occurred in the past. In regions devoid of historical or contemporary rockfalls, pre-existing rockfalls represent the only empirical proxy for evaluating local rockfall behavior and provide valuable input for rockfall modeling and risk assessment studies. Existing rockfalls provide important data for predicting rockfall volumetric, lithologic, and morphologic (i.e., boulder shape) characteristics, but a thorough consideration of landscape evolutionary chronologies (including deforestation) and post-emplacement mobility scenarios is required before pre-existing rockfalls can be confidently used as future spatial indicators.
Conclusions
The spatial distributions and physical–geological properties of individual
(n=1093) rockfall boulders deposited at two sites in Banks Peninsula prior
to the 2010–2011 Canterbury earthquake sequence (CES) are compared to
boulders (n=185) deposited during the CES. Pre-CES to CES boulder ratios
range between ∼5:1 and 8.5:1 respectively, suggesting preservation of multiple pre-CES rockfall events with a flux analogous to or smaller than CES events, and/or pre-CES event(s) of larger flux. Pre-CES and CES boulders at one site (Purau site) have statistically consistent power law frequency–volume distributions between 1.0 to >100.0 m3. At the Rapaki site, CES boulders have smaller and more clustered volumetric distributions that are less well fit by power laws compared with
the pre-CES data, interpreted to reflect variations in rockfall source
characteristics through time. Boulders of volcanic breccia (VB) have a
larger binned-percentage of large volume boulders and more equant boulder
aspects relative to coherent lava (CL) boulder lithologies at both sites,
revealing lithologic controls on rockfall physical properties. The maximum
runout distances for Rapaki CES VB and CL boulders are greater than that of
pre-CES boulders of equivalent lithologies, volumes, and morphologies. This
is interpreted as an effect of anthropogenic deforestation on the hosting
hillslope, which enabled CES boulders to travel further than their pre-CES
counterparts due to reduced resistance from vegetation. At Purau, isolated
geomorphic domains exhibit this same effect, however in other intra-site
locations, pre-CES boulder locations exceed runout distances of CES
boulders. This is interpreted to reflect post-depositional mobility of
prehistoric boulders via debris flows and other surface processes, reduction
of CES boulder runouts in channels due to collisional impedance from pre-CES
boulders, and heterogeneity in the CES boulder distributions, which reduced
the likelihood of large runout boulders occurring due to smaller volumetric
fluxes. The shadow angle method is a reliable predictor for pre-CES and CES
rockfall runout at both sites. At Rapaki, the pre-CES and CES rockfall data
are best fit using a 2nd order polynomial regression, while at Purau
rockfalls require a variety of data fits (e.g., linear, log, and polynomial),
suggesting intra-site geomorphic and geologic factors affecting rockfall
hazard are spatially variable. Bare-earth and forested numerical modeling
suggest that the majority of pre-CES rockfalls were emplaced before
deforestation of the Purau hillslopes and enable identification of boulder
sub-populations that have likely experienced post-emplacement mobility. The
RAMMS_3 model effectively shows the potential spatial extent of rockfalls that could result from more widespread detachment within the Purau source rock and provides a preliminary indicator of low-lying areas most susceptible to future rockfall hazard. More in-depth rockfall hazard analyses (including numerical rockfall modeling) are required at Purau and should consider the implementation of boulder morphologies, terrain parameters, and hillslope vegetation attributes developed in this study. Our research highlights the challenges of using rockfall distributions to characterize future rockfall hazards in the context of geologic and geomorphic variations, including natural and anthropogenically influenced landscape changes.
Data availability
The research data can be publicly accessed at 10.5061/dryad.9km1t86 (Borella et al., 2019).
Friction parameters chosen for each terrain type in RAMMS.
μminμmaxεDrag layerβκcoefficientVolcanic rock0.72.000.3500.5Loess and volcanic colluvium0.452.000.5300.6Loess0.32.000.5300.5Valley terrain0.22.000.9250.5
The total number of boulders with volume ≥ 0.1 m3 were
taken at runout distances of 1–10 m (yellow polygon 1), 30–40 m (yellow
polygon 2), 60–70 m (yellow polygon 3), and 100–110 m (yellow polygon 4)
from the volcanic source rock to estimate the total number of boulders in
areas near the source cliff where conditions were unsafe for continuous
mapping. The number of boulders in areas “b” and “c” were reduced by factors of 2 and 3, respectively, based upon field observations. The total number of rockfall boulders for the area (yellow dashed line) was normalized to a boulder size of 1.0 m3 using a power law frequency–size distribution (as determined at the Rapaki study location).
Conceptual diagram of hillslope illustrating the source rock cliff
and the talus slope. The reach angle (a) and shadow angle (b) are shown. Sketch modified from Evans and Hungr (1993), Wieczorek et al. (2008), and Copons et al. (2009).
Final resting locations for RAMMS_2 rockfalls assuming uniform forest density increase of 10 000 kg s-1. (Image is modified
after Land Information New Zealand, https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
Polygon shapefiles for runout terrain types. (Image is modified after
Land Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
Polyline shapefiles for RAMMS_1 rockfall source areas. (Image is modified after Land Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
Polyline shapefiles for RAMMS_2 and RAMMS_3 rockfall source areas. (Image is modified after Land Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
Polygon shapefiles for forest density. (Image is modified after Land
Information New Zealand,
https://data.linz.govt.nz/data/category/aerial-photos, last access: 6 March 2019.)
The supplement related to this article is available online at: https://doi.org/10.5194/nhess-19-2249-2019-supplement.
Author contributions
JB performed the field mapping, RAMMS modeling, and was the primary contributor to the data interpretation and paper authorship. MQ contributed to study design, data interpretation, and paper authorship. ZK performed field mapping, RAMMS modeling, and contributed to the preparation of the paper. KL conducted the source rock characterization at Rapaki. JA performed the strong ground motion analysis
and contributed to the preparation of the paper. LS, HL, and SL performed field mapping of rockfalls at Purau and/or Rapaki. SH and DG performed field work and contributed to the paper preparation.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Josh Borella thanks Louise Vick, Sarah Trutner, Peter Borella, Maxwell Borella, David Jacobson, Sarah Bastin, Jonathan Davidson, Peter Almond, Chris Massey, Simon Brocklehurst, David Bell, and Jarg Pettinga. Special thanks to Pip and David Barker for allowing land access in Purau and review of the Camp Bay geotechnical property report. We also thank the Rapaki landowners and farmers for land access.
Financial support
This research has been supported by Port Hills champion Sue Stubenvoll, the New Zealand Earthquake Commission Capability Fund, and Frontiers Abroad.
Review statement
This paper was edited by Thomas Glade and reviewed by Martin Mergili and Alexander Preh.
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